Semiclassical initial value representation propagation of vibrational wave functions

Two new semiclassical initial value representation (IVR) treatments of the time dependent wave function were described. As is the case for most IVR methods, the FPS expression for a system with N degrees of freedom contains integrals over all 2N phase space variables. However, the HPS expression contains integrals over only N such variables, raising the prospect of improved numerical efficiency. As such, the numerical results demonstrate that both the FPS and HPS techniques are capable of propagating initial ground and excited states of anharmonic as well as harmonic systems.